Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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round upon their centres with equal velocities, ſo as that two
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veables, which ſuppoſe for example to be two ſtones placed in the
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points B and C, come to be carried along the circumferences B G
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and C E, with equal velocities; ſo that in the ſame time that the
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ſtone B ſhall have run the arch B G, the ſtone C will have paſt the
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arch C E. </
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<
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>I ſay now, that the whirl or
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vertigo
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of the leſſer wheel
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is much more potent to make the projection of the ſtone B, than
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the
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vertigo
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of the bigger wheel to make that of the ſtone C.
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<
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>Therefore the projection, as we have already declared, being to be
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made along the tangent, when the ſtones B and C are to ſeparate
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from their wheels, and to begin the motion of projection from the
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points B and C, then ſhall they be extruded by the
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impetus
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ceived from the
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vertigo
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by (or along) the tangents B F and C D.
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<
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>The two ſtones therefore have equal impetuoſities of running
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long the tangents B F and C D, and would run along the ſame, if
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they were not turn'd aſide by ſome other force: is it not ſo
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gredus
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?</
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>SAGR. </
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>In my opinion the buſineſſe is as you ſay.</
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>SALV. </
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>But what force, think you, ſhould that be which averts
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the ſtones from moving by the tangents, along which they are
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tainly driven by the
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impetus
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of the
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vertigo.
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>SAGR. </
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>It is either their own gravity, or elſe ſome glutinous
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matter that holdeth them faſt and cloſe to the wheels.</
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>SALV. </
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>But for the diverting of a moveable from the motion
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to which nature inciteth it, is there not required greater or leſſer
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force, according as the deviation is intended to be greater or
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ſer? </
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<
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>that is, according as the ſaid moveable in its deviation hath a
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greater or leſſer ſpace to move in the ſame time?</
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>SAGR. </
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<
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>Yes certainly: for it was concluded even now, that to
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make a moveable to move; the movent vertue muſt be increaſed
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in proportion to the velocity wherewith it is to move.</
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<
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>SALV. </
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<
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>Now conſider, that for the deviating the ſtone upon
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the leſſe wheel from the motion of projection, which it would
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make by the tangent B F, and for the holding of it faſt to the
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wheel, it is required, that its own gravity draw it back the whole
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length of the ſecant F G, or of the perpendicular raiſed from the
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point G, to the line B F, whereas in the greater wheel the
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on needs to be no more than the ſecant D E, or the
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lar let fall from the tangent D G to the point E, leſſe by much
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than F G, and alwayes leſſer and leſſer according as the wheel is
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made bigger. </
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<
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>And foraſmuch as theſe retractions (as I may call
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them) are required to be made in equal times, that is, whil'ſt the
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wheels paſſe the two equal arches B G and C E, that of the ſtone
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B, that is, the retraction F G ought to be more ſwift than the
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ther D E; and therefore much greater force will be required for </
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